Alas, with synchronised AC systems it just isn't that simple! (as it would be with DC) Just having a higher voltage would cause the inverter to export reactive power (VAr) but not real power (kW). To export real power it must create a sinewave which is very slighly ahead of the sinewave from the grid....ie its trying to pull the grid faster, this causes it to export power.
No, it wouldn't. If it peaked at the same time it would be in-phase with the grid - there would be no phase angle difference & no power would transfer. Even if the magnitude of the sinewave were bigger it would still only export reactive power.
The inverter sinewave must be a few degress ahead of the grid sinewave & attempting to "pull it faster" in order to export real power.
Think about generator theory. Remember that when a generator is operating in parallel with the grid controlling excitation influences reactive power & the torque from the prime mover determines the real power - the prime mover is trying to pull the generator rotor out-of-step with the magnetic field created in the stator by the grid. This ripping apart of the two magnetic fields is what causes the generation of real power. A similar process has to happen with the inverter.
I believe in a paralleled generator situation like Adrian is talking about, he is correct.
When synchronizing generators to the grid, you increase the speed control to take on more real load. The actual generator speed does not change because it is locked to the grid frequency due to the circulating currents, however it will pick up more of the real power load.
To increase the paralled generator's reactive loading, you try to increase the generator's output terminal voltage.
I believe the grid tie inverters are designed to try to vary their output frequency to control how much real power they output. Obviously a KW sized unit will not pull the utility units off frequency, but they will try to unload them.